%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP483-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:34:30 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 85 unt; 4 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 120 ( 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),double_divide(X0,identity))),X1) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f12,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f13,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f14,definition,
sF2_fnc = multiply(a3,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f10,f14,f13,f12,f11]) ).
fof(f40,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f40]) ).
fof(f44,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f40,f9]) ).
fof(f45,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f40]) ).
fof(f53,plain,
identity = double_divide(double_divide(c3,sF1_fnc),sF0_fnc),
inference(paramodulation,[status(thm)],[f12,f44]) ).
fof(f55,plain,
identity = double_divide(double_divide(b3,a3),sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f44]) ).
fof(f68,plain,
multiply(sF1_fnc,double_divide(b3,a3)) = inverse(identity),
inference(paramodulation,[status(thm)],[f55,f40]) ).
fof(f78,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),double_divide(X0,identity))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f79,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,double_divide(X3,inverse(X3))),double_divide(X0,identity))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f78]) ).
fof(f80,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,identity),double_divide(X0,identity))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f9,f79]) ).
fof(f81,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(X2),double_divide(X0,identity))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f80]) ).
fof(f82,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(X2),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f81]) ).
fof(f83,plain,
! [X0,X1] : inverse(double_divide(double_divide(X0,inverse(identity)),double_divide(inverse(X1),inverse(X0)))) = X1,
inference(paramodulation,[status(thm)],[f8,f82]) ).
fof(f87,plain,
! [X0,X1] : double_divide(double_divide(double_divide(inverse(X0),inverse(X1)),identity),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f82]) ).
fof(f89,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(double_divide(X0,X1),inverse(X2)),double_divide(inverse(X3),multiply(X1,X0))),X2) = X3,
inference(paramodulation,[status(thm)],[f40,f82]) ).
fof(f92,plain,
! [X0,X1,X2] : multiply(X0,double_divide(double_divide(X1,inverse(X0)),double_divide(inverse(X2),inverse(X1)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f82,f40]) ).
fof(f93,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),inverse(X1)),double_divide(X1,inverse(identity))) = X0,
inference(forward_demodulation,[status(thm)],[f40,f83]) ).
fof(f95,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f87]) ).
fof(f96,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f40,f95]) ).
fof(f139,plain,
! [X0] : double_divide(inverse(identity),inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f45,f96]) ).
fof(f148,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f139]) ).
fof(f151,plain,
! [X0] : multiply(X0,double_divide(X0,inverse(identity))) = identity,
inference(paramodulation,[status(thm)],[f139,f93]) ).
fof(f159,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f148,f139]) ).
fof(f160,plain,
multiply(sF1_fnc,double_divide(b3,a3)) = identity,
inference(backward_demodulation,[status(thm)],[f148,f68]) ).
fof(f167,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),identity) = X0,
inference(paramodulation,[status(thm)],[f148,f96]) ).
fof(f177,plain,
! [X0] : inverse(multiply(identity,inverse(X0))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f167]) ).
fof(f178,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f41,f177]) ).
fof(f196,plain,
! [X0] : multiply(inverse(X0),identity) = inverse(X0),
inference(paramodulation,[status(thm)],[f159,f40]) ).
fof(f231,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(inverse(inverse(X0)))),
inference(paramodulation,[status(thm)],[f178,f196]) ).
fof(f236,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f178,f231]) ).
fof(f363,plain,
! [X0] : identity = double_divide(double_divide(identity,X0),X0),
inference(paramodulation,[status(thm)],[f236,f44]) ).
fof(f431,plain,
! [X0] : multiply(X0,double_divide(X0,identity)) = identity,
inference(forward_demodulation,[status(thm)],[f148,f151]) ).
fof(f432,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f431]) ).
fof(f437,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f432,f96]) ).
fof(f452,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f437,f159]) ).
fof(f454,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(backward_demodulation,[status(thm)],[f437,f363]) ).
fof(f488,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f40,f452]) ).
fof(f676,plain,
! [X0,X1] : double_divide(double_divide(double_divide(double_divide(double_divide(b3,a3),sF1_fnc),inverse(X0)),double_divide(inverse(X1),identity)),X0) = X1,
inference(paramodulation,[status(thm)],[f160,f89]) ).
fof(f680,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,inverse(X0)),double_divide(inverse(X1),identity)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f55,f676]) ).
fof(f681,plain,
! [X0,X1] : double_divide(double_divide(inverse(inverse(X0)),double_divide(inverse(X1),identity)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f437,f680]) ).
fof(f682,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),identity)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f452,f681]) ).
fof(f683,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(inverse(X1))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f8,f682]) ).
fof(f684,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f452,f683]) ).
fof(f707,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f684,f684]) ).
fof(f718,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f684,f40]) ).
fof(f745,plain,
double_divide(sF0_fnc,identity) = double_divide(c3,sF1_fnc),
inference(paramodulation,[status(thm)],[f53,f707]) ).
fof(f757,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f707,f40]) ).
fof(f761,plain,
inverse(sF0_fnc) = double_divide(c3,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f8,f745]) ).
fof(f899,plain,
! [X0,X1] : multiply(X0,double_divide(double_divide(X1,inverse(X0)),identity)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f454,f92]) ).
fof(f937,plain,
! [X0,X1] : multiply(X0,inverse(double_divide(X1,inverse(X0)))) = inverse(inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f899]) ).
fof(f938,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = inverse(inverse(X1)),
inference(forward_demodulation,[status(thm)],[f40,f937]) ).
fof(f939,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f452,f938]) ).
fof(f1044,plain,
! [X0,X1] : multiply(X0,X1) = inverse(multiply(inverse(X1),inverse(X0))),
inference(paramodulation,[status(thm)],[f96,f757]) ).
fof(f1062,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(inverse(X0),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f488,f1044]) ).
fof(f1317,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f718,f939]) ).
fof(f1321,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f452,f939]) ).
fof(f1447,plain,
! [X0,X1] : multiply(inverse(double_divide(X0,X1)),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f757,f1321]) ).
fof(f1451,plain,
multiply(inverse(b3),sF3_fnc) = c3,
inference(paramodulation,[status(thm)],[f13,f1321]) ).
fof(f1469,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f40,f1447]) ).
fof(f1488,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f452,f1469]) ).
fof(f1662,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f757,f1488]) ).
fof(f3197,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),multiply(X2,X0)),X1) = X2,
inference(backward_demodulation,[status(thm)],[f1062,f82]) ).
fof(f3336,plain,
! [X0] : double_divide(double_divide(double_divide(b3,inverse(X0)),sF1_fnc),X0) = a3,
inference(paramodulation,[status(thm)],[f11,f3197]) ).
fof(f4699,plain,
! [X0] : double_divide(double_divide(multiply(inverse(b3),X0),sF1_fnc),X0) = a3,
inference(forward_demodulation,[status(thm)],[f1662,f3336]) ).
fof(f4702,plain,
double_divide(double_divide(c3,sF1_fnc),sF3_fnc) = a3,
inference(paramodulation,[status(thm)],[f1451,f4699]) ).
fof(f4728,plain,
double_divide(inverse(sF0_fnc),sF3_fnc) = a3,
inference(forward_demodulation,[status(thm)],[f761,f4702]) ).
fof(f4729,plain,
multiply(sF0_fnc,inverse(sF3_fnc)) = a3,
inference(forward_demodulation,[status(thm)],[f1317,f4728]) ).
fof(f4749,plain,
multiply(a3,sF3_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f4729,f1488]) ).
fof(f4762,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f14,f4749]) ).
fof(f4763,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4762,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP483-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:14:49 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.14/5.43 % Refutation found
% 0.14/5.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.71/6.66 % Elapsed time: 1.066540 seconds
% 2.71/6.66 % CPU time: 0.382925 seconds
% 2.71/6.66 % Total memory used: 16.963 MB
% 2.71/6.66 % Net memory used: 16.162 MB
%------------------------------------------------------------------------------